ILHC and Electoral Systems

Well it’s been nearly 6 months since my last post here and I thought I should get it back going again. I was going to post something about teaching swing dance in Nepal, a recipe for vegetable curry or something similarly relevant but then the ILHC scores came out.

Now for those of you who have followed this blog you’ll note I’m slightly obsessed by both lindy hop and elections. ILHC presents a perfect opportunity to combine these two. All the scores of all the judges are published in addition to the complete rankings. It’s rare that in an election (which is what a competition with multiple judges is, they’re ‘electing’ the most skilled dancer/s) you’re presented with all the ballot papers.

So I thought I’d rerun the comp results using a variety of different voting systems for a bit of fun and to point out some of the quirks with different electoral systems.

First up let me just say that this is just a hypothetical. I’m not suggesting that ILHC should change the way they calculate the positions. A lot of people have spent way more time and effort than me evaluating scoring systems and came up with one that fits a lot of criteria and works for ILHC. For more on the Relative Placement Method used by ILHC, check here,here and here.

I’ve deliberately steered clear of systems like plurality (first past the post) and instant runoff voting (such as STV), which rely on first preferences and aren’t designed for circumstances where the ratio of voters to candidates is low. The two systems I’ve used are both designed for circumstances where all candidates receive a ranking from all voters.

The first is the Borda method. The raw ILHC scores are just that, scores. One could add them up to determine placings but this has problems, the judges may not be consistent in the spread of candidates scores (e.g. one might score all the way from 0 to 100, another might only go from 40-80). This is why the ILHC scores are converted to rankings before being combined. The Borda method converts those rankings back into scores and adds them together. The problem with Borda methods is that they are prone to being influenced by outlier scores and producing ties when you have a small voter pool.

The second is the Condorcet method. Condorcet methods are appealing for a dance contest because they simulate how some lindy comps (at least the finals) are run. These methods envisage a round robin series of head to head contests – whoever wins the most contests, wins the competition. The problem with Condorcet methods is that they tend to produce a lot of draws, particularly with a small voter pool. I’ve used the Small method to try and eliminate some of these draws, but the only way to fully resolve them is to have some sort of casting vote act as a tiebreaker. Note that the Small method returns the same results as the basic Condorcet method except where there are ties.

The full ‘results’ are at the end of the post but here’s my summary: In 6 of the events (Balboa J&J, Balboa Strictly, Open Advanced and Champions Strictly Lindy and Pro-Am) the alternative systems make no difference (I’ve included cases where ties are involved, provided that order is preserved). In another 4 (All Star J&J, Lindy Hop Classic, Showcase and Teams) the only differences were in placings below 3rd.

For four of the events the systems disagreed over the third place getter, in some cases significantly:

Open Jack and Jill – Both Borda and Condorcet placed the actual 3rd place into 5th, replacing them with 4th or 5th.

Advanced Jack and Jill – As with the Open Jack and Jill 3rd was switched with 4th or 5th.

However the two biggest upsets (i.e disagreements over 1st place) happened in what are arguably 2 of the 3 premier events for ILHC, Invitational Jack and Jill and Pro Lindy Hop Classic.

In the Pro Lindy Classic, Condorcet gives the same result for 1,2 and 3 as Relative Placement. Only Borda disagrees, switching first (Todd and Ramona) and second (Sarah and Dax) In this case what we’re really seeing is one of the failures of the Borda method, it is prone to influence in small voter pools of one or two outlier results.

For the Invitational Jack and Jill, both the Borda and Condorcet methods would place Sarah Breck and Pontus Persson first (who placed second), with Borda placing Peter Strom and Jo Hoffberg (who placed first) second and Condorcet Ramona Staffeld and Skye Humphries (who placed fourth). There’s also a lot of variation throughout the remaining placings.

What’s going on here? A glance at the scores for the Invitational J&J reveals substantial variation in the scores between individual judges. Nine out of the twelve contestants received a place (1,2 or 3) from at least one of the judges. This lack of consensus is exactly the sort of situation where differences in electoral systems become most pronounced. Perhaps in what some consider to be the pinnacle competition format in Lindy Hop (Jack and Jill simulating social dance) the skill level of the top international competitors is just so high that its becoming increasingly difficult to differentiate between them.

Your email address will not be published. Required fields are marked *

Comment

Name *

Email *

Website

Search for:

About Me

I'm a swing dancer, DJ and jazz music nerd living in Pavia, Italy. Once upon a time I was a physics geek so I like to talk about science too. This blog is about that and other musings on politics, philosophy and whatever strikes my fancy. Check me out on the tweets @lindypenguin